Finite Group Databasebeta

← #29580641

Subgroups — #29580641

Order 15616.

492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456591C211yesmaximal, characteristic
2#21455768C211yesmaximal, characteristic
3#21455763C211yesmaximal, characteristic
4#21445888C211yesmaximal, characteristic
5#21444182C211yesmaximal, characteristic
6#21443695C211yesmaximal, characteristic
7C61×#1472C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C2×#14519736C2211yescharacteristic
10#16840104—22no—
11#16840100—22no—
12#16840098—21no—
13#16840097—21no—
14#16840095—21no—
15#16840095—21no—
16#16840093—21no—
17#16840090—21no—
18#16840001—22no—
19#16839918—21no—
20#16839917—21no—
21#16839804—21no—
22#16839802—21no—
23#16839772—21no—
24#16839771—21no—
25#16839726C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27#16839516—22no—
28#16839487—22no—
29C2×C22⋊Q8×C61C2211yescharacteristic
30C61×#407C2211yescharacteristic
31C2×C22⋊C8×C61C2211yescharacteristic
32C61×#324—22no—
33C22×Dic122D411yescharacteristic
34C2×#11758202—22no—
35C2×#11758194—21no—
36C22×#92418D412yes—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40#14519756—21no—
41#14519736—21no—
42#14519736—21no—
43#14519736—21no—
44#14519736—21no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×C4⋊Dic61D411yescharacteristic
47C2×C4⋊Dic61D411yescharacteristic
48C2×#11758196—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C4×Dic61—21no—
52#14519711—22no—
53#14519710—22no—
54#14519710—22no—
55#14519709—22no—
56#14519708—22no—
57#14519702—22no—
58#14519702—22no—
59#14519701—22no—
60#14519701—22no—
61#14519701—22no—
62#14519700—22no—
63C22⋊#92418—21no—
64C22⋊#92418—21no—
65C22⋊#92418—21no—
66C22⋊#92418D412yes—
67C22×Q8×C61D411yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C2×M16×C61—21no—
70C22×C8×C61—21no—
71C22⋊Q8×C61—21no—
72C22⋊Q8×C61—21no—
73C22⋊Q8×C61—21no—
74C22⋊Q8×C61—21no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61D411yescharacteristic
77C2×C22⋊C4×C61—21no—
78C22⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61D412yes—
82C24×C61#4111yescharacteristic
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—42no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—42no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C2×Dic122—21no—
100C2×Dic122—21no—
101C2×Dic122—42no—
102M16×C61—42no—
103C2×C8×C61—22no—
104C2×C8×C61—42no—
105C2×C8×C61—41no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊Dic61—41no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115C22⋊Dic61—41no—
116#11758202—82no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123#11758196—41no—
124#11758196—41no—
125C4×Dic61—41no—
126C4×Dic61—41no—
127#11758194—42no—
128C2×#92418—22no—
129C2×#92418—22no—
130C2×#92418—42no—
131C23×C61—22no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61#12111yescharacteristic
135C23×C61#12111yescharacteristic
136C23×C61#12111yescharacteristic
137Q8×C61—42no—
138Q8×C61—42no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—81no—
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12011yescharacteristic
152C2×C4×C61#12711yescharacteristic
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—42no—
160C2×Dic61—81no—
161Dic122—42no—
162Dic122—42no—
163C8×C61—42no—
164C8×C61—81no—
165#92418—42no—
166#92418—42no—
167#9979—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—82no—
177C22×C61#39211yescharacteristic
178C22×C61#47312yes—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—81no—
183C4×C61—81no—
184C4×C61#45812yes—
185Dic61—81no—
186Dic61—81no—
187Dic61—81no—
188Dic61—81no—
189#3189—611no—
190#3095—611no—
191#3095—611no—
192#1818—611no—
193#1472—611no—
194#1472D6111yescharacteristic
195#1293—611no—
196C2×C61—22no—
197C2×C61—41no—
198C2×C61—41no—
199C2×C61#201711yescharacteristic
200C2×C61#202011yescharacteristic
201C2×C61#202211yescharacteristic
202C2×C22⋊Q8—611no—
203C2×C22⋊Q8C2×D6111yescharacteristic
204C2×#117—611no—
205#485—1222no—
206#485—1222no—
207#484—1221no—
208#484—1221no—
209#484—1221no—
210#484—1221no—
211#483—1221no—
212#483—1221no—
213#467—1222no—
214#451—1221no—
215#451—1221no—
216#428—1221no—
217#428—1221no—
218#419—1221no—
219#419—1221no—
220#407—611no—
221#407C2×D6111yescharacteristic
222C2×C22⋊C8—611no—
223C2×C22⋊C8C2×D6111yescharacteristic
224#336—1222no—
225#324—22no—
226#324—1222no—
227C61#997911yescharacteristic, complemented, Sylow
228C22×Q8—611no—
229C22×Q8D24411yescharacteristic
230C23×C4C22×D6111yescharacteristic
231C2×Q16—1222no—
232C2×M16—21no—
233C2×M16—1221no—
234C22×C8—21no—
235C22×C8—612no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—1221no—
241C22⋊Q8—1221no—
242C22⋊Q8—1221no—
243C22⋊Q8—1221no—
244#117—1221no—
245#117—1221no—
246#117—1221no—
247#117—1221no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4D24411yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C42—1221no—
258#107—1222no—
259#107—1222no—
260#107—1222no—
261#106—1222no—
262#106—1222no—
263#103—1222no—
264#103—1222no—
265#103—1222no—
266#103—1222no—
267#103—1222no—
268#103—1222no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—612no—
273C22⋊C8—1221no—
274C22⋊C8—1221no—
275C22⋊C8—1221no—
276C22⋊C8C22⋊D6112yes—
277C24#1175822211yescharacteristic
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—42no—
281C2×Q8—1221no—
282C2×Q8—1221no—
283C2×Q8—2442no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4C2×D24411yescharacteristic
292C22×C4D4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C22×C4C2×C22⋊D6111yescharacteristic
297Q16—4882no—
298M16—42no—
299M16—2442no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—41no—
303C2×C8—1222no—
304C2×C8—1222no—
305C2×C8—2442no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C42—2441no—
325C42—2441no—
326C23—22no—
327C23—41no—
328C23—41no—
329C23#1451975011yescharacteristic
330C23#1451975011yescharacteristic
331C23#1451975111yescharacteristic
332Q8—42no—
333Q8—42no—
334Q8—2442no—
335Q8—2442no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—4881no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4#1451974511yescharacteristic
355C2×C4#1451974711yescharacteristic
356C2×C4#1451974711yescharacteristic
357C2×C4#1451977311yescharacteristic
358C8—42no—
359C8—81no—
360C8—2442no—
361C8—2442no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—82no—
371C22#1683967111yescharacteristic
372C22#1684003612yes—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—4881no—
379C4—4881no—
380C4—4881no—
381C4—4881no—
382C4#1683995312yes—
383C2—22no—
384C2—41no—
385C2—41no—
386C2#2144692311yescharacteristic
387C2#2144693911yescharacteristic
388C2#2144694911yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1472C2
socleC22×C61#392
prime radicalC24×C61#41
hypercenter#1472D61
hypocenterC61#9979
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
227. C61#9979semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214565912
#214557682
#214557632
#214458882
#214441822
#214436952
C61×#14722
#997961